Question

1 1/7+5 5/7 3 1/5+5 2/5 7 1/7+3 2/7 9 3/8+7 1/8 5 13/15+1 1/15 3 11/19+7 7/19

Answer 1

11/7+5 5/7=7 2/7
3 1/5+5 2/5=8 3/5
7 1/7+3 2/7=10 3/7
9 3/8+7 1/8=16 1/2
5 13/15+11/15=6 3/5
3 11/19+7 7/19=10 18/19

Answer 2

To calculate the sum of the given fractions, we need to find a common denominator for all of them. In this case, the common denominator is 105, which is the product of all the denominators.

Now, let's add the fractions step by step:

1 + 1/7 = 7/7 + 1/7 = 8/7 5 + 5/7 = 35/7 + 5/7 = 40/7 3 + 1/5 = 15/5 + 1/5 = 16/5 5 + 2/5 = 25/5 + 2/5 = 27/5 7 + 1/7 = 49/7 + 1/7 = 50/7 3 + 2/7 = 21/7 + 2/7 = 23/7 9 + 3/8 = 72/8 + 3/8 = 75/8 7 + 1/8 = 56/8 + 1/8 = 57/8 5 + 13/15 = 75/15 + 13/15 = 88/15 1 + 1/15 = 15/15 + 1/15 = 16/15 3 + 11/19 = 57/19 + 11/19 = 68/19 7 + 7/19 = 133/19 + 7/19 = 140/19

Now, we can add all the fractions together:

(8/7) + (40/7) + (16/5) + (27/5) + (50/7) + (23/7) + (75/8) + (57/8) + (88/15) + (16/15) + (68/19) + (140/19)

To add fractions with different denominators, we need to find the least common multiple (LCM) of the denominators. In this case, the LCM is 420.

Now, let's convert all the fractions to have a denominator of 420:

(8/7) * (60/60) = 480/420 (40/7) * (60/60) = 2400/420 (16/5) * (84/84) = 1344/420 (27/5) * (84/84) = 2268/420 (50/7) * (60/60) = 3000/420 (23/7) * (60/60) = 1380/420 (75/8) * (52.5/52.5) = 3937.5/420 (57/8) * (52.5/52.5) = 2992.5/420 (88/15) * (28/28) = 2464/420 (16/15) * (28/28) = 448/420 (68/19) * (22/22) = 1496/420 (140/19) * (22/22) = 3080/420

Now, we can add all the fractions together:

480/420 + 2400/420 + 1344/420 + 2268/420 + 3000/420 + 1380/420 + 3937.5/420 + 2992.5/420 + 2464/420 + 448/420 + 1496/420 + 3080/420

To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD), which in this case is 4:

(480/4)/(420/4) + (2400/4)/(420/4) + (1344/4)/(420/4) + (2268/4)/(420/4) + (3000/4)/(420/4) + (1380/4)/(420/4) + (3937.5/4)/(420/4) + (2992.5/4)/(420/4) + (2464/4)/(420/4) + (448/4)/(420/4) + (1496/4)/(420/4) + (3080/4)/(420/4)

Now, we can simplify the fractions:

120/105 + 600/105 + 336/105 + 567/105 + 750/105 + 345/105 + 984.375/105 + 748.125/105 + 616/105 + 112/105 + 374/105 + 770/105

Finally, we can add the fractions together:

(120 + 600 + 336 + 567 + 750 + 345 + 984.375 + 748.125 + 616 + 112 + 374 + 770)/105

Calculating the numerator:

Numerator = 120 + 600 + 336 + 567 + 750 + 345 + 984.375 + 748.125 + 616 + 112 + 374 + 770 = 7192.625

The sum of the given fractions is:

7192.625/105 ≈ 68.55

Therefore, the sum of the given fractions is approximately 68.55.